Question

what is the y-intercept of the function?
$f(x) = 3x^2 + 5x + 9$
the y-intercept is \square. (type an ordered pair, using integers or decimals.)

Explanation:

Step1: Recall the definition of y-intercept

The y - intercept of a function \( y = f(x) \) is the point where the graph of the function intersects the y - axis. On the y - axis, the x - coordinate is 0. So, to find the y - intercept, we substitute \( x = 0 \) into the function \( f(x) \).

Step2: Substitute \( x = 0 \) into the function \( f(x)=3x^{2}+5x + 9 \)

When \( x = 0 \), we have \( f(0)=3(0)^{2}+5(0)+9 \).
First, calculate \( 3(0)^{2}=3\times0 = 0 \), \( 5(0)=0 \). Then \( f(0)=0 + 0+9=9 \).

The ordered pair for the y - intercept is \( (0,f(0))=(0,9) \) since the x - coordinate is 0 and the y - coordinate is \( f(0) = 9 \).

Answer:

\((0, 9)\)